This continuous distribution is characterized by having the same probability for any value of the interval. It is widely used for contributions of type B uncertainties in which only the major and minor dimensions of the interval are known, for example in the division or resolution of a digital instrument. In many cases this distribution can also be assigned when there is little information about the random variable, in bibliographic data or when the coverage factor of an uncertainty is not known,
The general formula of this distribution is defined for all values of x for which A ≤ x ≤ B, according to the equation:
Input parameters:
- Average. Average value of the random variable.
- Semi-interval. Corresponds to the middle of the interval to which this distribution is applied, that is (B-A) / 2, where A and B are the upper and lower bounds of the interval. If this function is applied to the uncertainty by resolution of a digital instrument, this parameter will correspond to half of the minor division (d / 2). Sometimes it also applies to analogic instruments taking the appreciation (or estimation) as if it were an estimated division, beyond which it is no possible more visual information. In this case the semi-interval will be e / 2.
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This distribution is the one that most frequently is representing natural and social events. Much of the evidence from classical statistics, as well as the estimation of uncertainties, is based on the assumption that the data conform to a normal distribution. From the theoretical perspective, the Central Limit Theorem maintains that given a random sample of sufficiently large size, it will be observed that the distribution of means follows an approximately normal distribution. The general formula of this distribution is:
This distribution represents random variables whose logarithms are distributed according to a normal distribution. The lognormal distribution takes different forms depending on the value of its scale parameter and is often used in the reliability of high technology products and also in microbiological counts since they are based on the multiplicative growth model.
This continuous probability distribution in the field of positive reals is intimately related to the Normal distribution, for example, it is the sample distribution of σ². The Xi (or Chi) Square distribution is defined with a single parameter which are degrees of freedom. The function is always asymmetric and biased to the right. This distribution is very frequently used in various branches of science since it allows analyzing data sets and determining if the difference between them is due to chance (null hypothesis) or to another external factor.
This distribution is a continuous function in the domain of positive real numbers, frequently used in economics, meteorology and telecommunications, as well as other specific applications, such as the reliability rate or the survival of organisms or machines. The random variables that have the Weibull distribution model the distribution of faults in systems when the fault ratio is proportionally related to a power of time. This distribution is defined from a characteristic Form (> 0) parameter that would indicate the failure rate, so that if the failure rate decreases, it is constant or increases with time. That corresponds with if the parameter k is smaller, equal or greater than 1.
The Cauchy distribution has the particularity of being of the Gaussian type of distributions, however it has the highest peak and the tails decompose very slowly. Although MCM Alchimia suitably generates the pseudo-random samples for this distribution, the results graph will look like an isolated peak since the abscissa axis of it is taken in the 99% coverage probability interval. Because the decay of the tails is so gradual, the range of significant probabilities becomes very narrow.
The distribution of Von Mises is a continuous function of the circular calls, that is, they are defined for the real ones in the interval from 0 to 2p. This function is currently used preferably in the field of epidemiology to describe the spread of diseases or technological applications such as signal processing. The Von Mises distribution is also known as normal circular as it is similar to Gaussian, but restricted to the circular plane.
The NegBinomial distribution is discrete distribution, defined in the domain of positive integers. It is similar to the binomial distribution except that the n parameter refers to non-total and incomplete events. In other words, a random variable with NegBinomial distribution of parameters n and p represents the number of successes whose probability is p, which are achieved in a sequence of n failed trials. The parameters by means of which this distribution is defined have the same form as those that represent the Binomial distribution, although, as we said, the parameter n represents a different quality.
Dies ist eine diskrete Verteilung, deren Domäne die Menge positiver Ganzzahlen ist, die die Anzahl der in einer Folge von n Versuchen erzielten Erfolge darstellt. Diese Tests müssen dichotom sein, dh sie bieten nur zwei Möglichkeiten (Erfolg und Misserfolg) und haben eine definierte Erfolgswahrscheinlichkeit = p.
The Poisson distribution is a discrete distribution defined for the domain of integers greater than zero. It is used mostly to represent the probability that a certain number of events will occur in a period of time, a defined distance, area, volume, etc.,